package com.zhugang.week13.dp;

/**
 * @program algorithms
 * @description: maxValue
 * @author: chanzhugang
 * @create: 2022/09/13 00:56
 */
public class MaxValue {

    /**
     * 剑指offer 47 礼物的最大值
     * https://leetcode.cn/problems/li-wu-de-zui-da-jie-zhi-lcof/
     *
     * @param grid
     * @return
     */
    public int maxValue(int[][] grid) {
        /**
         * 最值问题：第一时间肯定想到dp， 定义状态、找状态转移方程
         */
        // dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]) + grid(i, j)

        int m = grid.length;
        int n = grid[0].length;

        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];

        // 初始化第一行值
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

        // 初始化第一列值
        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                // 状态转移方程
                dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }

        return dp[m - 1][n - 1];
    }

}